Probability Definition and 1000 Threads

Hi folks - I need some help with a tricky probability. Here's the situation: Let's say there are 4M internet users in Age Group A. (The total set) Of those 4M, there are 1,000 users who play a specific sport. Those 1,000 are spread evenly over 125 teams, so 8 players each. 1. What's the...

2) The Agency for Healthcare Research and Quality reported that 53% of people who had coronary bypass surgery in 2008 were over the age of 65. Fifteen coronary bypass patients are sampled. a) What is the probability that exactly 8 of them are over the age of 65? b) P (less than 10 are over...

Apologies in advance for my ignorance, I don't really have a reference to consult and Google hasn't been too helpful! In standard probability theory there are a few common useful formulae, e.g. for two events ##S## and ##T## $$P(S\cup T) = P(S) + P(T) - P(S\cap T)$$ $$P(S \cap T) = P(S) \times...

I decided to take cases.For example-:A gets one 1 duck and B gets 2,3,4,...,51.So i can write this as 50C1(1/2)5051C2(1/2)51+50C1(1/2)5051C3(1/2)51+... But i was unable to solve it further. please help.

A person picks 8 cards without replacement from a bag containing cards numbered from 1 to 6 (117 in total). What is the probability that the sum of those 8 cards is 28? Given that P(1)=8/117, P(2)=14/117, P(3)=34/117, P(4)=39/117. P(5)=14/117 and P(6)=8/117.

Here's the problem: A chef made 500 cookies randomly mixed with 1000 nuts including 600 almonds and 400 hazelnuts in which each nut is the same size. Suppose the number of pieces of nuts in a piece of cookie follows a Poisson distribution. (a) Suppose cookies are randomly selected one-by-one...

My approach is the amount of successfull options / total amount of options. I can first pick white in 3 different ways. Then black in 4 different ways 3 * 4 But I can also pick black first then white 4 * 3 Total amount of ways to pick marbles are 7 *6 So the probability is: (3*4 + 4 * 3) / (7...

I calculated <+|Φ> to be (1-√2i)/4√2 + (3-2i)/4√2. When I squared this I for 16/32 but this is no the right answer.

Hi, I am trying to understand the calculation in the following research paper: http://cramton.umd.edu/market-design/abdulkadiroglu-sonmez-house-allocation.pdf

Hi, I want to frame the above Probability question for computer science students. I have stated my idea above but I want to refine it so that it becomes a more comprehensive real world problem. Zulfi.

Suppose we have a code: 4457 If these numbers are randomly drawn what are the odds of drawing those numbers? Here's my approach: The available numbers range from 0123456789 and there are four columns, minus the numbers which were drawn gives: 1/(10^4-4)~0.01% Now what about the odds of...

I set hN(1)hN(1) equal to cNcN, but I'm confused on how I'd be able to solve it and because of that I was not able to conclude that 0 is recurrent when qx/px = infinity

Problem: A vertex set $S$ in a graph $G$ is said to be totally t-dominating, for a positive integer t, if $|N(v) \cap S| \geq t$ for all $v \in V (G)$. Suppose that r, t, n are positive integers such that $r > 2t$ and $t \geq \frac{14}{3}\cdot ln(2n)$, and let $G$ be an r-regular n-vertex graph...

This is probably a stupid question but i don't want to make a stupid mistake here, so i thought better ask: I'm starting with the simple free Schrödinger Equation ##V(x)=0## (can be 1 dim) and an initial condition where the wave function is somehow constrained to be entirely localized around a...

So back in the other thread I asked about compatibility of classical probability theory (PT) and QM – and it turns out there is no inherent reason why they need to be incompatible. Therefore I was looking for something that makes them compatible, which wasn’t easy to search for. But there seems...

The probability should be ## (1/6)^k * (5/6)^{20-k} ## But the book says the answer is : ## \begin{pmatrix} 20 \\ k \\ \end{pmatrix} * (1/6)^k * (5/6)^{20-k} ## Because there are 20 over k different sequences, but the order doesn't matter? I just don't understand why the 20 over k is there...

I know how to calculate the probability of finding the particle in a region by integrating the mod square of the wave function within that region. But in this question only the operator is provided but not the wave function. I am not sure how am I supposed to proceed with this problem.

I am not sure what I can do with the equation. I realize that ## \vert c_1 \vert ^2 = \vert c_2 \vert ^2 = \frac{1}{2} ## does not mean that ## c_1 ^2 = c_2 ^2 = \frac{1}{2} ## or that ## c_1 = c_2 ##, so I don't know how to use it. I think ideally I might have something like ##P = \vert c_1...

a. P(X = 3) = (4/6) x (4/6) x (4/6) x (2/6) = 8/81 b. X ~ Geo (2/3) Is this correct? Thanks

Suppose we have four games and the probability that a player will win the game are as follows: Game 1: 71% Game 2: 55% Game 3: 58% Game 4: 16% Suppose player b won these games with the following percentages of time: Game 1: 100% Game 2: 96% Game 3: 87% Game 4: 67% In other words, he's a very...

I was studying statistical mechanics when I came to know about the Boltzmann's entropy relation, ##S = k_B\ln Ω##. The book mentions ##Ω## as the 'thermodynamic probability'. But, even after reading, I can't understand what it means. I know that in a set of ##Ω_0## different accessible states...

In these lecture notes about statistical mechanics, page ##10##, we can see the graph below. It represents the distribution (probability density function) of the kinetic energy ##E## (a random variable) of all the gas particles (i.e., ##E=\sum_{i}^{N} E_{i}##, where ##E_{i}## (also a random...

I need to predict an upcoming rogue wave or analyse old rogue wave events using simple probability models and real-time data for a physics high school project.

Hey! :o We have data of a sample of $100$ people from a population with standard deviation $\sigma=20$. We consider the following test: \begin{align*}H_0 : \ \mu\leq 100 \\ H_1 : \ \mu>100\end{align*} The real mean is $\mu=102$ and the significance level is $\alpha=0.1$. I want to...

I found out that the operator H is not a Hermitian operator but I didn't understand the second part of the question. What do I calculate the probability of?

1. Definition If E and F are two events associated with the same sample space of a random experment, the conditional probability of the event E given that F has occurred, i.e. P(E|F) is given by P(E|F) = (E∩F)/P(F) (P≠0) 2. Properties of conditional probability Let E and F be events of...

Hello, I am trying to learn the basic concepts of calculating probability as it pertains to dice rolling. I have searched the internet and not been able to figure it out. If I have a regular 6 sided dice and I want to know the probability of rolling a 3, I know its 1/6 or 16.6%. This is...

Attempt: I'm sure I know how to do this the long way using the definition of stationary states(##\psi_n(x)=\sqrt{\frac {2} {a}} ~~ sin(\frac {n\pi x} {a})## and ##\int_0^{{a/2}} {\frac {2} {a}}(1/5)\left[~ \left(2sin(\frac {\pi x} {a})+i~ sin(\frac {3\pi x} {a})\right)\left( 2sin(\frac {\pi x}...

(a) I find the geometric distribution $$X~G0(3/8)$$ and I find p to be 0.375 since the mean 0.6 = p/q. So p.g.f of X is $$(5/8)/(1-(3s/8))$$. (b) Not sure how to find the p.g.f of Y once we know there are 6 customers?

Because I do have a background in the latter it was originally very difficult for me to understand some aspects of QP (quantum physics) when I initially learned it. More specifically whenever probabilities were involved I couldn’t really make full sense of it while I never had any problems...

I think both Jane and Bill are carriers. I'm unsure if the answer is 1/4 (25%).

If anyone could help me understand how Peebles gets from line one of the autocorrelation to the second line, I'd be most grateful. I don't understand what identity or property is being used to go from a product in the expectation value to a sum in the expectation value.

I am trying to estimate probability of loosing (probability of bankrupt ##Pb##) using Martingale system in betting. I will ilustrate my problem on the following example: Let: ##p## = probability of NOT getting a draw (in some match) We will use following system for betting: 1) We will bet only...

Show that ##v_{av}=\frac{\hbar k_2 + \hbar k_1}{2m}## is equal to ##v_{av}=\frac{\omega_2 - \omega_1}{k_2-k_1}##. Which of the identities listed above (if any) would make the sign change between ##k_2## and ##k_1##? One can attain a "wave packet" by superposing two or more sinusoidal waves...

Given the upper data, if the nominal value for capacitance is 33nF and tolerance of 20%, then values can range between 26.4nF and 39.6nF. With the bottom margin being set at 30nF, this means that the interval takes approximately 72% of all values. Is this the correct procedure to solve this...

Would like to know what method, or distribution to use when solving a problem like this:I start from level 0. There is a probability p chance to drop to level -1 and a (1-p) chance to increase to level 1. The levels range from level -n to level n. When it reaches level -n or level n, it resets...

a) P(X<18) = (18-20)/sqrt25 =-2/5 =-0.4 then you use the standard normal table and find that; P(X<18)=0.3446 b) P(X>27) = (27-20)/5 = 7/5 = 1.4 P(Z>1.4) =P(Z<-1.4) =0.0808 C) =(13<X<23) =13-20/5 , 23-20/5 =-7/5 , 3/5 =-1.4 , 0.6 P(Z<0.6)-P(Z<-1.4) =0.7257-0.0808 =0.6449

There's an event which is joined by 240 members. The Event Organizer prepares 30 doorprize with one of them being the main ones. If Mr. Aziz's family has 15 tickets, the probability that Mr. Aziz gets the main doorprize is ... A. 1/16 B. 1/8 C. 1/4 D. 1/2 I thought the answer was 15/240 (the...

Suppose we have a gas in the room at some temperature which is room temperature or higher. In some references the probability is given by -ΔS, which is indeed a tiny number and makes sense. However, in other references the probability is given by the Boltzmann factor plus the number of...

My attempt: case 1: get one vowel (A) from word HOORAY = 1/6 x 2/3 x 4/5 = 4/45 case 2: get one vowel (A) from word MATHS = 3/6 x 2/3 x 1/5 = 1/15 case 3: get two vowels (2A) from word HOORAY and MATHS = 1/6 x 2/3 x 1/5 = 1/45 Total probability = 8/45 Answer key = 1/3 Where is my mistake...

Consider a qubit. Given a state equation, how to calculate the probability of finding spin in +x direction?

Hi all, Sorry, in my first message, I posted this question in the Basic Probability section, and so I moved it to this section. I have a surface (for example, a blank paper). In this surface, I have some elements of the set "A" randomly distributed. In this surface, I also have some elements...

How do I find the probabilty density function of a variable y being y=ab, knowing the probabilty density functions of both a and b? I know how to use the method to calculate it for a/b - which gives 1/pi*(a²/b²+1) - using variable substitution and the jacobian matrix and determinant, but which...

For the probability of finding R out of N (indistinguishable) bosons in one half of a volume with a total of 2g states (g in each half) I get the following expression: PR = WR / WT where WT is the number of ways of distributing N particles in the total volume: WT = (N+2g-1)! / (N! (2g-1)!)...

A) (0.5)-(0.3) =0.2 b) c) i have no clue how to determine from just a set of numbers if they are independant or mutually exclusive

In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current...

I calculated the complex conjugate of both the given wavefunctions. For ψ1: ∫re^((-2)mod(r)x)dx=1 with upper limit ∞ & lower limit -∞. I replaced the upper and lower limit after breaking down the function inside integration as follows- r*∫e^(2rx)dx from -1/r to 0 and r*e∫e^(-2rx)dx from 0 to...

I have the following two problems that I need to solve: 1. Suppose that the service time for a student enlisting during enrollment is modeled as an exponential RV with a mean time of 1 minute. If the school expects 500 students during enrollment period, what is the probability that the...

Hello everyone. Let us consider 3 events A,B,C such that: $$P((A \cap B )\cup C)=P(A)*P(B)*P(C)$$ Notice that the second term is a union and not an intersection. Are they independent? And what if the assumption was: $$P(A \cap( B \cup C))=P(A)*P(B)*P(C)$$? I know that the independence condition...